Whatever the problem is, it's unlikely to be your iptables. You have a default policy of ACCEPT on the OUTPUT chain and your only rule there jumps to the PETER chain which contains only one rule that allows outbound connections to ports 25025-25050 on the remote server. If it matches that rule then the connection will be allowed and if it doesn't match then it'll return from "PETER" to OUTPUT and will then take the default "ACCEPT" as there are no more rules. So whatever happens, the connection is allowed from your side.

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